When I first got my GCC in 2008 she was housed with a parrotlet. The previous owner had them together. We let them stay together for about a month after bringing them home, to let them settle in. It was a process separating them as they were very bonded. We did it slowly, moving their cages further and further apart.
The parrotlet barbered his own feathers, and he would even go as far as to chew all the feathers on my GCC off as well. That was one of the reasons we separated them. The other reason was that, even though we never witnessed any aggressive behaviour between the two of them in the month or so we had them together, we thought the size difference was too dangerous to risk. Parrotlets are such small little birds.
If you must get a companion for your current GCC I would stick with the same species. And even then you are not guaranteed that they will get along.